The Crusaders announced last week they would be considering a change to their name and branding following the attacks that killed 50 people and left dozens injured, insisting the status quo is "no longer tenable".
The name has been seen as insensitive by many, given its links to the military campaigns launched by Christians against Muslims during the medieval period.
The branding and pre-game mascots, which feature knights riding on horseback in chain mail, waving swords and with crosses on their chests, have also come under scrutiny.
However opinion has been heavily divided among fans, and Crusaders' supporter Shane Cannons started an online petition calling on the franchise to keep its name. He said he hoped he was not the "only one".
Already the petition had nearly gained 25,000 signatures.
Cannons said the team was changing its name "because the Government thinks it's a good idea".
Prime Minister Jacinda Ardern told Newstalk ZB's Mike Hosking this morning "none of that is true".
"I haven't even expressed an opinion privately let alone publicly. I checked in with [Sports Minister] Grant Robertson as well and he hasn't either."
Crusaders CEO Colin Mansbridge told Radio Sport while the Government had shown interest in the process, there had been no instruction.
"They have been really clear they don't have an opinion, of if they do it is personal and they are leaving us to take care of it."
While there was "no pressure" from the Government, the franchise was receiving pressure from "many parts of the community" over the name.
"It has crystallised opinions."
The Christchurch-based Super Rugby franchise announced on Wednesday last week they would engage independent research company, Research First, to seek feedback and provide recommendations on the Crusaders team name and brand.
It would involve asking if they should change anything, if they should refine the imagery and branding but keep the name, or change the name and rebrand.
"Once we have feedback on those questions we will consider those last two options."
They were hoping to complete the process "as quickly as possible", but it would not be before the end of the 2019 season.
Mansbridge has previously said they were committed to taking the process seriously and doing the right thing.
"This is an event that rocked our community and brought some important issues to the fore," Mansbridge said. "One of the contentious issues that has been brought up in the aftermath of the Christchurch attacks is the name of our rugby team – the Crusaders.
"Because of our desire to be the best we can be and to support our community, we are treating the question around the appropriateness of our brand extremely seriously.
"We are committed to undertaking a thorough process, taking into account all relevant opinions and, most importantly, we are committed to doing the right thing."
New Zealand Rugby CEO Steve Tew said the Crusaders name and branding was "no longer tenable".
"In the wake of the Christchurch attacks, it is apparent that the symbolism the club has used, combined with the 'Crusaders' name, is offensive to some in the community due to its association with the religious Crusades between Christians and Muslims.
"Maintaining the status quo in terms of the Crusaders name along with the current imagery of knights on horseback is, in our view, no longer tenable because of the association with the religious Crusades that has now been drawn. That is therefore not one of the options that we will be considering."
Crusades reference point for white supremacists
Massey University professor of sociology Paul Spoonley, who has studied the behaviours of the rising far-right and white supremacist movement in New Zealand, previously told the Herald the crusades were a common point of reference for modern-day white supremacists.
"The white supremacists and the extreme right certainly refer back on occasion to the crusades. That's part of the history that they want to call upon in order to remind people that there is a global struggle against Islam.
"That's not necessarily connected to the Crusaders rugby team … [but] on a symbolic level, absolutely. But it's a bit like a number of the rest of us, we'll be saying to ourselves 'I had no idea. I did not realise that what I was doing was feeding into those groups who might be Islamophobic'. So it's that naivety again I think."
Spoonley said the process was not about cleansing history of anything which might could offensive, but having a discussion to understand why it's offensive, and to whom.
"I think we do need to have a discussion. And I agree entirely with the Crusaders management that you need to pick your moment to have that discussion and you need to involve members of the Muslim community in that discussion.
"It might be that Muslim community says 'No that's fine'. I don't know that, but you wouldn't want to continue just using that imagery without having that discussion."
In 2009, Middlesex County Cricket Club in England changed their name from the Middlesex Crusaders to the Panthers after only receiving "one or two" complaints from Muslim and Jewish communities.
